Asymptotics of a Free Boundary Problem
نویسندگان
چکیده
As was shown by Kaper and Kwong Diierential and Integral Equations 3, 353{362], there exists a unique R > 0, such that the diierential equation u 00 + 2 + 1 r u 0 + u ? u q = 0; r > 0; (0 q < 1, 0) admits a classical solution u, which is positive and monotone on (0; R) and which satisses the boundary conditions u 0 (0) = 0; u(R) = u 0 (R) = 0: In this article it is shown that u(0) is bounded, but R grows beyond bounds as q ! 1. 1 The Problem In 1], the reaction-diiusion equation u + u 1=2 ? 1 = 0 was proposed as a simple model for Tokamak equilibria with magnetic islands. The equation motivated a study of free
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تاریخ انتشار 2007